During the laying of a pipeline with the known vessel, a pipe section is first positioned in the firing line and then positioned in and engaged by the alignment device. The alignment device is used to align the pipe section with the pipeline suspending from the J-lay system. Subsequently, the aligned pipe section is connected to the pipeline. A disadvantage of the known pipelaying vessel is that the laying of the pipeline is slow. The use of this type of pipelaying vessel is extremely expensive and therefore every second of reduction in the critical production cycle time results in a large advantage.